Nonlinear Dynamic Analysis For Laminated/FGM Plates And Shells With Damage Under Low Velocity Impact

In this dissertation, considering the effect of nonlinear factor and environment conditions synthetically, the dynamic response, impact resistance, matrix damage, interfacial damage of the laminated composite/functionally graded plates and shells under low velocity impact are studied, and the essential characters of the mechanical and damage property are illustrated precisely. The research results are not only contribute to enrichment and development of contact theory and impact resistance research, but also have an important meaning in the practical engineering. The main results contain as follows.Based on the geometric nonlinear theory of the moderately thick shallow spherical shells and the damage theory,the constitutive relation for the laminated shallow spherical shells with matrix damage and matrix-fiber shear damage was established by employing a strain-based failure criterion.And a set of nonlinear equations of motion for the cross-ply laminated moderately thick shallow spherical shells under the low velocity impact were derived.By using the orthogonal collocation point method and the Newmark method to discrete the unknown variable functions in space domain and in time domain respectively,the whole problem is solved by the iterative method synthetically.The numerical results show that the damage,the initial velocity of the striking object and the shell's geometrical parameters all affect the contact force and the dynamic response of the structure under the low velocity impact to some extent.Based on the Reddy's higher-order shear theory and Talreja's damage model with tensor internal variables, the displacement field and Von Karman geometrical relations as well as the damage constitutive relations of the composite plate with matrix damage are established. When considering the variation of the normal contact force as well as the tangential contact force, the relations between contact force and contact deformation are founded by using Hertz contact model, and subsequently oblique impacting dynamic model of the composite plate are established. The nonlinear motion equations are solved by applying finite difference method, Newmark-βand iterative methods synthetically. In numerical examples, the effects of the impacting angle, initial velocity of the impactor and geometrical size on the nonlinear dynamic response and damage evolution of the composite laminated plate are investigated. Based on the elasto-plastic mechanics, the damage analysis and dynamic response of an elasto-plastic laminated composite shallow spherical shell under low velocity impact are carried out. A yielding criterion related to spherical tensor of stress is proposed to model the mixed hardening orthotropic material, and accordingly an incremental elasto-plastic damage constitutive relation for the laminated shallow spherical shell is founded when a strain-based Hashin failure criterion is applied to assess the damage initiation and propagation. By using a modified elasto-plastic contact law to establish the dynamic impacting model, and applying the presented constitutive relations and the classical nonlinear shell theory, a set of incremental nonlinear equations of motion for the axisymmetric laminated cross-ply moderately thick shallow spherical shell are obtained. In numerical examples, the effect of damage, elasto-plastic deformation and geometrical parameters on the contact force and the dynamic response of the structure under low velocity impact are investigated.The contact model of A.E.Giannakopoulos's 2-D functionally graded material (FGM) contact model is applied to predict contact force of shallow spherical shell with FGM coating under low velocity impact. And the interfacial damage analytical model is established based on the damage model of cohesive domain of the continuum damage theory. The nonlinear governing equations of motion for the shallow spherical shell substrate and FGM coating are obtained by Reissner variation. The questions are solved by using the orthogonal collocation point method, the Newmark method and the iterative method synthetically. In numerical examples, the dynamic response of shallow spherical shell with FGM coating and contact force are obtained and the effects of the functionally graded material index, the coating thickness, and geometrical parameters of FGM coating on interfacial damage and contact force are discussed.By applying steady-state heat conducting equation, the temperature field in FGM shallow spherical subjected to a uniform temperature load on the surface of shell and the temperature varies along the thickness direction are obtained. Then based on the contact model of Giannakopoulos's 2-D functionally graded material (FGM), a modified contact model is put forward to deal with impact problem of the functionally graded shallow spherical shell in thermal environment,in which the deformation of impacted sphere is considered. The displacement field and geometrical relations of the FGM shallow spherical shell are established on the basis of Timoshenko–Midlin theory. And the nonlinear equations of motion for the FGM shallow spherical shell under low velocity impact and thermal environment in terms of displacement variable functions are founded. Using the orthogonal collocation point method and the Newmark method to discretize the unknown variable functions in space and in time domain, the whole problem is solved by the iterative method. In numerical examples, the contact force and nonlinear dynamic response of the FGM shallow spherical shell under low velocity impact are investigated. The effects of temperature field, material and geometrical parameters on contact force and dynamic response of the FGM shallow spherical shell are discussed.The damage constitutive relations of the anisotropic materials are established by applying the continuum damage theory. Dividing the FGM plate to N sub-plies, and assuming the material property and damage are constant along the thickness of every single layer, the damage constitutive relations of the FGM plate with the elastic modulus varying along the thickness of the plate as the power law function are founded. By using the subroutine VUMAT of ABAQUS software, the constitutive relations of the FGM are embedded, and consequently the nonlinear dynamic property and damage of the FGM plate under low velocity impact are investigated by using the finite element software ABAQUS. The effects of the functionally graded material index, the impact velocity and the geometrical size on the nonlinear dynamic response and the damage of structure are discussed.